| Topic | Problem | Solution |
|---|---|---|
| None | If $f(x)=\int_{x}^{13} t^{2} d t$ then \[ f^{\pri… | Given the function \(f(x)=\int_{x}^{13} t^{2} dt\), we are asked to find its derivative \(f^{\prime… |
| None | A soccer ball is kicked from the ground with an i… | The maximum height of the ball can be found by finding the vertex of the parabola represented by th… |
| None | Let $A(t)$ represent your bank account balance, i… | Translate the problem into a mathematical model. The problem states that the bank account balance, … |
| None | A population tries to grow exponentially but is l… | Given the differential equation \(\frac{d P}{d t} = \frac{k}{M} P(M-P)\), where the continuous grow… |
| None | Suppose $f^{\prime}(x)=-7 x^{10}+4 x^{5}-7 x^{3}+… | Given the derivative of a function as \(f^{\prime}(x)=-7 x^{10}+4 x^{5}-7 x^{3}+8\) |
| None | On the Pluto, the acceleration due to gravity is … | The general equation for the height of an object under constant acceleration is given by \(h = h_0 … |
| None | If $\int f(x) d x=(-5 x-9)^{15}+C$, find $f(x)$ \… | The question is asking for the derivative of the function \((-5x-9)^{15}+C\). The derivative of a f… |
| None | A baseball player swings and connects with a pitc… | The problem provides the equation \(H=-16 t^{2}+80 t+4\) which represents the height of the ball (i… |
| None | An economist hired by a company that makes a popu… | The profit function is a quadratic function. The maximum value of a quadratic function is at its ve… |
| None | Suppose that the marginal revenue for firefightin… | Set the marginal revenue equal to the marginal cost: \(263 - 2x = 2.5x + 11\). |
| None | Expand. Simplify if possible. Assume that all var… | Given the expression \(\log _{4}\left(\frac{x y}{z t}\right)\) |
| None | \begin{tabular}{|c|c|} \hline Cones Sold & Profit… | The table shows a linear relationship between the number of cones sold and the profit. |
| None | Khan Academy Get Al Guide Donate [ Quiz 1 ¿ Googl… | Differentiate the given equation with respect to n: \( W'(n) = -0.05 \) |
| None | In a hotel chain, the mean number of rooms is 98 … | Given that the mean number of rooms in the hotel chain is 98 and the standard deviation is 4. |
| None | Find the derivative of the function. \[ r(t)=\fra… | The problem is asking for the derivative of the function \(r(t)=\frac{1}{2}(8t^2+t)^{-3}\). |
| None | Find the third derivative of the given function. … | Given the function \(f(x)=\frac{3}{x^{2}}\), we can rewrite it as \(f(x)=3x^{-2}\) to apply the pow… |
| None | Find the derivative of the function. \[ \begin{ar… | The problem is asking for the derivative of the function \(f(x)=(4-x)^{6}\). The derivative of a fu… |
| None | Based on the results of an extensive market resea… | Based on the results of an extensive market research study, an economist predicts that consumers in… |
| None | Find the third derivative of the given function. … | Given the function \(f(x)=4 x^{5}-3 x^{4}+4 x^{2}-2 x+6\) |
| None | (1) Khan Academy Get Al Guide Donate [ Quiz 1 Goo… | Substitute \(t = 0\) into the equation \(S=-0.25 t+4 \) |
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